Problem: Multiply the following complex numbers: $({1+5i}) \cdot ({4i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1+5i}) \cdot ({4i}) = $ $ ({1} \cdot {0}) + ({1} \cdot {4}i) + ({5}i \cdot {0}) + ({5}i \cdot {4}i) $ Then simplify the terms: $ (0) + (4i) + (0i) + (20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (4 + 0)i + 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (4 + 0)i - 20 $ The result is simplified: $ (0 - 20) + (4i) = -20+4i $